NONE! I have repeatedly told you this. I have never used more than one sample at a time. I have depended on the analysis of others. I cannot see how I can make this any clearer. I shall ignore all future questions on this because I cannot see any point repeating myself any further.

I already listed all the periodicities that I know of that Tifft reported in the 1970s. Subsequently he developed a theory and then began to find additional periods related to that theory. I have ignored that later work as possibly being selective.

The Tomes list from the Harmonics Theory was originally posted to usenet in 1994. It was also on my web site from that time. I repeat this original list here now.
Shortly after I made this comment:

In other papers Tifft mentions 2.67 km/s also.

As far as I can remember Tifft published the paper on CMBR basis in AstroPhys Journal also. I know nothing about the 18 km/s galactic expansion. It was not in any of the papers that I read. Maybe this came later. I have not done any analysis of the newer surveys, and agree that much more data is available. That was one of the questions I came to the forum to ask about getting data. I do not want to get 100 GB of data! Just a modest amount is quite sufficient. Perhaps when these discussions have run their course it would be appropriate for someone to advise me and assist me through the various steps in getting a modest sized sample or two for analysis. If that proves fruitful, them the same technique can be applied on larger volumes of data.

For straight forward galaxies with a single redshift, the easiest way to look at periodicity is as in the survey that I quoted with the 128 Mpc period --- to pick a sample that is in a small region of the sky (so called pencil beam) because then you do not have to worry about our motion relative to CMBR or anything else like that. Ideally the central redshift should be to better than 1 km/s. This can be repeated with many small areas of sky, the same consistent set periods should result, but in different directions there will be different starting offsets. When the whole sky is examined these starting offsets should be cleary explained by our CMBR motion.

Having stated that, I suspect that Tifft's 18 km/s figure may be some sort of bias in the CMBR due to our nearby galaxy centre in one direction. He may have found that this extra component brings all the different directions into better agreement. I am just guessing based on his earlier work.

I certainly think that it is a good idea to replicate Tifft's work. The only case I know of this being done was by Guthrie and Napier who did not find a 72 km/s period but did find a 37.6+/- 2 km/s period or something like that. It agreed with the 36 km/s one of Tifft's. But again the sample was much smaller than available today.

Much of the early work on the 72 km/s period came from single galaxy clusters where it was found that the differences in velocities were often 72 km/s or multiples thereof.

I do not know about Tiffty's bistates as already stated. My guess is that you can take a galaxy spectrum and by correlating it against a typical galaxy spectrum and varying the red shift adjustment continuously get a graph which has peaks at more than one place. This is standard variance analysis and i assume this technique is used when multiple absorptions at different redshifts are detected fro quasars. I have downloaded a few spectra to try and do this, but as far as I could tell they were all random noise and had no resemblance to anything at any red shift.

I missed this one before. This background I am about to give is necessary to answer your question. It is also of interest in seeing how I got to the redshift periodicities.

Originally I had no such concept in the harmonics theory and so had a problem of how to deal with the redshift. I first tried to address this by assuming that as the redshift velocity gos from 0 to c there will be the occurence of all the harmonics, so that e.g. the h=2880 one which is very strong will give c/2880 = 104.095 km/s. This didn't fit anything and stumped me for a while. Then I realized that Einstein's velocity addition formula for 104 km/s repeated 2880 times would not give c, indeed even repeated 1000000 times it would not. So I understood that you cannot get redshift periodicities by dividing by c. Because c really represents the result of adding an infinite number of any finite sized step together.

So I looked at how can you get a standing wave that is finite. It occurred to me that a wave which had extent over a distance to which z=1 would have an exact ratio of 2 in the wavelengths at the two places. Because harmonics theory says that standing waves produce 2x frequency, and this distance gives 1/2 frequency (i.e. 2 x wavelength) there is a feedback cycle. So I took the z=1 distance as the fundamental wave. From the Einstein velocity addition formula you can deduce that over that distance if the wave is divided in to h parts by the h harmonic then the relationship is (1+z)^h=2. When I understood that, and put in h=2880 I then got 72.15 km/s and I knew that I had a sensible solution. Then I calculated all the other strong harmonics giving the table that I just posted. I already found lists of redshifts that seemed to show several of the longer periodicities like the ~8600 km/s one.


It was a bit later that I realized that because at the nuclear scale energy is always moving to smaller waves (harmonic frequencies) then the mass of particles must grow over time. However if all particles have the same wavelength then they cannot easily do that because the waves going into one particle are the same ones coming out of others that are far away. This is not an easy problem to solve. In the end I understood that multiple frequencies are there at the same time and that one gets stronger and another gets weaker. At some point there will be sufficient stress on the wave structure to flip to a new state. When this happens to just a single atom, we see it as a photon being emitted or absorbed. When it happens to the whole solar system in a short time we see it as a mass extinction event because most of the life probably gets internally microwaved in a short period of time.

The funny thing with the harmonics theory is that you get a whole set of sine waves and add them up, but the answer is not what you expect. It is not a wavy line. It is near enough a horizontal line with vertical lines sticking up from it. It is rhythm. The bist that stick up are like a ruler in inches, where the 1/2" and 1/4" and 1/8" each stick up a bit less. But a bit more complicated than that. Here is an example graph. It has the time axis horizontally and the amplitude vertically and I split it into 12 equal sections to show how self similar it is in 1/12s.


This gives the best idea that I can give of answering your question. It is only one dimensional but we have to imagine space and time filled in this way. It shows multiple levels of periodicities. You can see some big steps that repeat and some medium ones and some small ones. The periodicities are like that and the jumps in mas will show a similar pattern. Many small jumps and some medium and few large ones. But always in steps from the periodicities listed.

You might like to calculate the mass difference between a proton and a neutron for fun and divide that difference into the proton mass. See if it comes out near to a strong harmonic.

Here are some statements, by rtomes, in this thread (post number given in the 'Posted by' line):Here are some extracts from the Tifft ApJ paper referenced above:rtomes, did you read Tifft's "Astrophysical Journal Vol 221 Pg 756-775 1978 May 1" paper?

Thank you for the clarification.

In light of your clarification, what status does anything you have posted in this thread, re quasars, have (in a scientific sense)?

I asked this question once before, and I seem to have missed your answer; if you already answered it, please point me to that answer; if not, please answer it.

An extension and clarification: what (ATM) claims, if any, are you making wrt quasars?

ETA: perhaps I did miss the answer; is it in post #90?

Could you please point out the post(s) in which you answered this question? If you haven't yet answered it, please do so now.Comment: it would seem that the main Tifft paper cited (concerning "periodicities") was either not read, or misunderstood (see previous post).

If we cannot establish the consistency link between the key Tifft paper and your ATM ideas, starting with an unambiguous definition of the key term (the redshift of a galaxy), how can we even begin to evaluate (much less question or challenge) claims such as this?

The work that I did on redshift periodicities was in 1994. There may well have been things in the papers that did not sink into my mind. I was concentrating on the periodicities that he found. If I had read these later after thinking about the mechanisms of redshift change in steps then I might well have paid more attention to these matters.

I have simply been honest about what I know about and what I don't, as requested. You need to understand that the redshift periodicities is just one of very many areas of cycle research that I studied. Also I am 60 years old now and do not always remember everything perfectly accurately.

UPDATED

Sorry. In rereading this the bistates is simply meaning a 36 km/s periodicity not a 72 km/s one. Yes I did understand about this from Tifft but just did not remember the term. What I wrote previously about bistates was nonsense. My apologies for that.

You can collect the various periodicities reported by Tifft in the 1970s as I did. That way you check that I didn't do any selection. That I do not know everything about the relevant astronomical details is not important to a sensible statistical test. What matters is that there is no biased selection. I think that it is important to only use Tifft's data from before the time at which he developed his own theory, to avoid any possible contamination from that theory.

Then you can check my calculations of the harmonics up to say a million easily if you want to. This has already been done by Pete Brown in Australia (who also pointed out that my harmonics calculation is the same as a known series) and so I am sure that they are right.

Then you can use the formula (1+z)^h=2 to solve for z from each of the strong harmonics that are calculated. The result ought to be the graphic that I posted with the various z values (and some zc values for comparison to redshifts quoted in km/s).

You can then do a statistical check on the matching of the two sets in the range ~100 km/s to ~2 km/s which is the range in which Tifft reported periodicities.

Tifft was certainly not aware of the harmonics theory when he determined his values because it hadn't been invented for another 10 years after that.
I was not aware of any but the 72 km/s periods when I derived my formula, but anyway you can see that it is a very simple formula and cannot be engineered to fit Tifft's data.

I will describe that test in more detail because it is central to my claim. I used the list of harmonics that I posted to usenet and posted here recently. You can see from my graph that the 2.67 km/s period reported by Tifft is present in my graph but was not in that list because it was below the threshhold that I went to. I suggest sticking to that same threshhold because that list was made without awareness of Tifft's work. You may still be able to find some of these posts in usenet archives, but I do not think that matters.

If you look at the Tifft values, taking an average where he reports a similar value several times (e.g. 7.99 and 8.05 would be averaged to 8.02 km/s). Then the Tifft values can be put next to the Tomes list for obvious matches. The percentage differences should be determined in each case. I think that you will find that all are within 0.5% of my figures. However the figures range over a wide set of sizes, and it is easier to understand the percentages differences as being the best test if the logs of all the figures are taken, both mine and Tifft's. Then the figures are more or less evenly spread over an interval from log(100) to log(2) (in km/s). So we make the null hypothesis assumption that either Tomes figures are nonsense or Tiffts figures are nonsense. In case of either being nonsense there is no reason for them to agree with each other.

So the test is to be a chi-square test where the Tifft values are considered as falling within a percentage of the Tomes figures. The percentage is the one thing that is chosen to best fit the data so we say that it is a chi square test with 1 degree of freedom. If the percentage is 0.5% then the intervals are established about the Tomes figures of 0.5% which in log terms means plus or minus log(1.005) about each figure. This chosen range is therefore equal to just this proportion of the whole range: (log(100)-log(2))/log(1.005)/2/9 where the 9 is the number of figures in my list and the 2 is the two sides (+ and -) that we consider the values being within. This answer is that the defined interval is just 1/39 of the entire available space in the (log) range from 2 to 100 km/s.


In fact you find that nearly all the Tifft values fall in this tiny window. I think that it might be 6 out of 6 in the first few papers and maybe 8 out of 9 between all the 1970s papers. The formula for chi-square needs an estimate how many would fall in each region according to the null hypothesis. If there are 9 values then we would expect 9/39 in a region that is 1/39 of the Tifft values in the region within 0.5% of the Tomes values and the other 9*38/39 in the remainder. These values give expected values of 0.23 and 8.77 wheras the observed are (I think) 8 and 1.
Chi square is defined as sigma (o-e)^2/e where e=expected and o=observed. That gives a result of chi-square = 269.4 for 1 d.f.
My chi-square table has for d.f.=1, p=0.1 x2=2.706, p=.05 x2=3.841, p=.02 x2=5.412, p=.01 x2=6.635. You can see that the value 269.4 is a long way further up the table.

Actually, in Section II of this paper, Tifft states very clearly that "bistates is simply [...] a 36 km/s periodicity not a 72 km/s one" is "inconsistent with the internal models of galaxies in DSR1 where a state spacing of 70-75 km s^-1 is clear and no significant amount of 36 km s^-1 periodicity is seen." And Tifft spends quite a few pages in this paper explaining his 'states' model and how he analyses the data to show consistency with his model. Do I correctly understand your post (which I have quoted here) to say that you reject Tifft's 'state' model but accept "a 36 km/s periodicity" despite your rejection?

Alternatively, if you accept this 'state' model, please state (summarise) the good observational results which are evidence for it.

I also asked about the ~18 km/s "galactic expansion" in Tifft's paper - would you like me to repeat, or clarify, my question on this?

Could you please clarify this?

Specifically:

* what do you consider "Tifft's data from before the time at which he developed his own theory" to be?

* how did you conclude that Tifft's 'state model' was not a theory?

* how did you establish the validity of the reported ~72 km/s redshift periodicies conclusions (derived results) in terms of the long chain of assumptions and calculations that these derived results seem (to me) to depend upon*?It seems that this whole exercise rests upon an assumption, or postulate, (or similar): that the derived conclusions (about a ~72 km/s redshift periodicity) stated in Tifft's paper are valid, in some scientific sense. I understand from your posts in this thread that you are claiming that they are ... are you making such a claim?

Note that if you are making such a claim (which is most assuredly an ATM one), then I trust that you will be able to answer direct, pertinent questions on that claim.

If you are not making such a claim, then what ATM claim are you making?

*This is the third time I am asking you this question; if you don't understand it, please ask for clarification.

(my bold)

It seems in 1994 rtomes was very familiar with the ~18 km/s "galactic expansion" Tifft claimed in his 1978 paper.

How well does the Tifft conclusion re "the true motion of the solar system" match post-HIPPARCOS, mainstream estimates (for the LSR and the peculiar solar motion)?

rtomes: I am not familiar with the term "blends".

Nereid: [snip] Perhaps a simpler question might be: given a perfectly accurate redshift of a galaxy (we'll look at definitions later), which Tifft declares to be not a "monostate", how is a specific redshift period/quantum determined?

rtomes: Arp has reported galaxies that show discontinuities in their redshift profiles of 72 km/s. IMO this would happen when a galaxy is in the process of shifting from one state to the next and would be a bit like water freezing or something like that. It would begin somewhere and spread out as a wave, though there might be a few leaders and laggards. This data of Arp's is hard to explain any other way. Sorry, I do not have a reference for that.

Nereid: If you don't have a reference for it, what merit should this have, in any scientific investigation?

For example, I could claim that "[t]his data of Arp's" was all made up, late one evening after a too many pints at the local pub. Without a reference, how can anyone reading this decide, objectively, whose story is right?

rtomes: Of interest is something else that just came to mind. Have a look at the average rotational velocity of the inner planets relative to the Sun. They show clear 12 and 6 km/s multiples. Most are very close with only Venus off by 1 km/s. Also an analysis of nearby star radial velocities shows a slight tendency to more being at multiples of 12 km/s.

Nereid: What sources are you using, as inputs to your analysis?

Historically the 72 km/s period was found first and a number of papers on that published. I saw an article about the 72 km/s in New Scientist which set me to trying to understand it in terms of Harmonics theory. The whole problem of course is that if you interpret it as velocity, then the earth is in a special place. No-one really believes that. That is why Tifft's work is disregarded. However Arp's explanation of redshifts being steps in time not velocity totally solves the problem of geometry and our unique position - it looks the same everywhere. But I do not think that astronomers have generally understood this. Furthermore I think that their analysis of redshifts looking for distance correlations are all contaminated by that lack of understanding of Arp. That is why I want to do my own analysis with the newer data.

I do distinguish between Tifft's periodicity findings ("quanta" in his words) and his interpretations. In particular his theory was an attempt from chaos theory to explain the pattern because it has many frequency doublings. However chaos theory does not produce the combined pattern of 2s and 3s found and harmonics theory does. e.g. in km/s
72 36 18 9 ratios of 2 across
24 12 6 3 and 3 down
I think that your suggestion (if I understand it correctly) that the state model is interpretation or theory, rather than just pure observation, is a correct one. I think it is based on the history of the 72 km/s period being known for some time and then suddenly some 36 km/s steps turning up. And they did again for Napier and Guthrie. Evenetually when he found the other periods of 12, 6, 3 km/s etc then he saw the pattern clearly.

If you look at my post #94 in this thread then you will see the pattern that is expected from Harmonics teoery. If you just pick out the biggest peaks you will see a single large quantum. If you then look at the next biggest peaks you will find some smaller quanta of 1/2 and 1/4 that size and eventually 1/12 that size. This is the result of getting better data and including smaller galaxies in the sample. In the local region I have found that the smaller galaxies are at distance steps of 1/12 of the Andromeda distance, or 2,220,000 / 12 = 185,000 LY. That is pretty close to the Magellanic cloud distances from our galaxy centre. Other nearby small galaxies are at multiples of this distance from us or from M31 or M33 etc.

I am aware that to some extent harmonics theory is spilling into this thread. I suppose that does not matter a lot. It is difficult to not address those issues because they do suggest why Tifft's periods should be taken very seriously.

There is an article at http://www.obspm.fr/actual/nouvelle/jul04/merc.en.shtml that shows some solar system dynamics over many millions of years. The 1.11 million year cycle is evident even in the orbit of Mercury. Lasker is the world expert on long term solar system dynamics.

LOL!

It doesn't matter what source you use for the planets. The planetary data are known to high accuracy. You just have to use v=2*pi*r/t where r=mean radius of planets orbit and t=orbital time.
For the inner planets you get in km/s Me=47.9, Ve=35.0, Ea=29.8, Ma=24.1 and from memory Ceres is close to 18.0. When looked at as multiples of 6 km/s, the deviations are 0.1, 1.0, 0.2 and 0.1, all extremely small except venus which is a little off.

For the stars I used a catalogue, but I won't present this as it is not as strong a case as the others. I just mention it as these things are all pervading. Once you have done all this with me you will probably start to notice these values popping up everywhere.

Hi Nereid

My turn to ask some questions.

I have presented in the quantized red shift thread the case for Tifft's periodicities and my calculated redshift periodicities being extremely significantly similar according to a chi-square test. This one item on its own outweighs many other things, although of course many astronomers reject Tifft's results. I suggested that the reason for that is that it seems to imply a special place for the Earth. But putting all that aside, I have suggested that the null test is:
*** Tifft's results are spurious OR Tomes theory is of no use ***
This is an inclusive OR so that it means that either is wrong or both are wrong. I think that this would be the view of many astronomers. Am I right?

I propose to prove that the null result will be rejected at the ~p<10^-18 level
(I cannot be exact here as I cannot find a chi-square table that goes far enough). Do you agree that if the null result is rejected that it means that both results are correct. That Tifft's values are real and Tomes theory is useful? (This is only a question in logic so it should be easy).

My argument goes like this. You probably need to accept that I did not develop my theory until after Tifft published his results, otherwise Tifft could have fiddled his data to match my results. If he had he would probably agree with me which he does not. I didn't start on my harmonics theory work until 1984 and got the theory worked out in 1989 and the redshift part in 1994. I state that I only knew about the 72 km/s quantum at that time, but my logic does not depend on that fact.

If Tomes theory is good but Tifft's values are spurious then there is no reason for them to agree with each other. Do you agree?

If Tomes theory is wrong and Tiffts's values are real there is no reason for them to agree with each other. Do you agree?

If both are useless there is still less reason for them to agree with each other. Do you agree with that?

If Tomes theory is right and Tifft's data is meaningful then we are not surprised if they agree with each other.

All that is required then is to establish that my table of redshift periods are indeed the strongest harmonics calculated as explained on my web pages and using the redshift formula (1+z)^h=2. There is no chance that the table is a fiddle if someone checks the maths. Do you agree?

For Tifft's data I suggest using any periods that he clearly states and published prior to 1980. I believe that all the significant quanta had been mentioned by that date. Where several values have been reported the average should be used. I think that this is an unbiased procedure. Do you agree?

I think that it is important that someone other than me searches Tiffts papers in the range ~1975 to 1979 inclusive in AstroPhys Journal for any mentioned periods. That assures that I have not biased the results. Do you agree?

I can do chi-square calculations but it is essential that an independent statistician should check the results. Do you agree?

If the result is extraordinarily significant, do you agree that this establishes both Tifft's and Tomes' work as sensibly established and worthy of further study?

If you think this sounds too much in one go, you might want to just get a statistician to tell you how significant the chi-square result is first.

regards
Ray

Moderator note: Moved from the Harmonics Theory thread, per the OP’s request.

I did an answer to a similar question before I though.

In the simplest case you need a number galaxies in nearly the same direction. Then taking the measured redshifts you perform a type of spectral analysis. The simplest method is to consider a test periodicity such as 72 km/s and to then take the remainders of the redshifts after removing multiples of 72 km/s. If you plot a histogram of the remainders from each galaxy, the null hypothesis is that they will be randomly distributed. If there is a periodicity then they should be heaped up in a smaller region of the range. By varying the test periodicity in small increments and plotting the resulting heaping up, you get a graph that has peaks at the potentially valid periods. These need to be tested for significance.

My description is trying to make clear the idea. There are simpler mathematical ways of doing it, even in a spreadsheet, that give a sensible measure. The result is very similar to a spectrum from either a spectrometer or a spectral analysis like FFT.

Yes, I accept that references are needed. Unfortunately I did not always keep records of references in my early work and even when I did, I made about 40 notebooks full of stuff, so I cannot always find them. These things are still useful as notes, because someone who sees them may see an explanation of make a connection and go search it out. I did a quick web search without success.

Can you list some please (other than the Tifft one already on the table)?

If possible, please focus on those which are in relevant peer-reviewed journals, and which present original analyses or observations.When* you get around to answering some of the questions I've asked about how Tifft derived "the 72 km/s", it may become obvious why his work was disregarded (in a nutshell, no such period exists ... at least in the input data he used).As I have said, at least once before, this assumes that there is, indeed, a redshift periodicity.

If and when you choose to put the relevant Arp papers (concerning redshift periodicity in galaxies) on the table, BAUT members will be able to question and challenge your claims. Until you do, what point is there in repeating unsubstantiated claims?It seems that my questions are not sufficiently clear; let me try again.

In post #80, I listed a number (8) of assumptions, or inputs, Tifft made, or used, in converting observations into a (derived) conclusion of a ~72 km/s redshift periodicity.

In post #83, you agreed that several of these (~4) were indeed used, and are important. You stated you were not familiar with "blends", nor with the ~18 km/s "galactic expansion" (3 assumptions). You stated that one assumption was "not needed" (a galactic co-ordinate system). You stated that, as far as you knew, there were no other assumptions.

Subsequently you have stated your interpretation of Tifft's "redshift state" model, several times, and I have continued to challenge you on that understanding, by referring directly to Tifft's paper (more to come).

In post #92, you quoted yourself on a Tifft claim that requires "galactic expansion, at least locally" (or, to quote Tifft directly "π = -18.8 km s^-1"). I have asked you, several times, in differently worded questions, how the validity of the ~72 km/s redshift periodicity depends on the existence of such "π = -18.8 km s^-1", but you have yet to answer.

In post #101, I asked the (general) question again, in two different ways:I will return to "the existence of a "static universal frame"", "suitability of "the galactic coordinate system" to determine "the solar motion"", "absolute accuracy (however defined) of "the galactic coordinate system" Tifft used", and "techniques for uniquely removing the "[internal] rotational or radial motion components" of the galaxies" soon.

If you do not understand the questions I am asking, about either the importance of the assumptions, or the actual assumptions themselves, please ask for clarification.

If you need more time to answer them, please say so (and give an indication of when you expect to answer them).

If you do not know the answer to a question, please say so.References please, both "Napier and Guthrie" and Tifft (?) - "Evenetually when he found the other periods of 12, 6, 3 km/s etc"How are the so-called ~72 km/s redshift periodicities related to the distance to M31 and the distance to the LMC and SMC?If I may paraphrase (and turn up the contrast): the scientific validity of Tifft's conclusions (concerning ~72 km/s redshift periodicities) is much less important than the fact that your ATM idea includes a number close to this.

Or, turning this around and making it a question, given the importance you attach to ~72 km/s, how important is it to establish the scientific validity of Tifft's conclusions?

*or if; I have been trying to focus on the validity of the astronomical evidence you have presented to support your ATM claims in this thread (currently the so-called 72 km/s redshift periodicity). It wouldn't surprise me if this thread ends - 30 days after it was started - with many basic questions about such evidence still unanswered.

Thanks for the clarification.

However, it seems that your method is quite different from the one Tifft reported using, to arrive at conclusions about redshift quantisation, in his 1978 paper.

For example:So, I will ask my question again:

Given a perfectly accurate redshift of a galaxy (we'll look at definitions later), which Tifft declares to be not a "monostate", how is a specific redshift period/quantum determined?

This time I have highlighted a key part of the question which you seem to have overlooked.

Please explain, in detail, how a specific redshift period/quantum can be extracted from the "observed mean redshift of a galaxy" (which galaxy is not a monostate), given that (in Tifft's model) this observed redshift "can in principle lie anywhere between state values, depending on the number and distribution of states present" (my bold).

Indeed.

And they are all multiples of 0.1 km/s, with no deviation whatsoever.

And 0.2 km/s, with only two with deviations.

And 0.3 km/s (all within 0.1 km/s)

And 0.4, 0.5, 0.6, 0.8, 0.9, 1.0, ...

But if the predictions are 'exact', then only the first (multiples of 0.1 km/s) is consistent; given the accuracy of the input numbers, even a single deviation of 0.1 km/s is surely fatal to the hypothesis?If you wish to retract the claim, please say so.

If you do not retract the claim, please substantiate it.Indeed.

And I can find the following sequences of digits in the base-10 expression of pi:
1234567890
0987654321
1111111111
2222222222
24082007
....

I can find extremely strong correlations between things like the RA of Pluto and the GDP of the USA.

And so on.

What does any of this numerology have to do with science (in general) and astronomy (in particular)?

Some initial comments:

To what extent is this an example of, or a variation on, "correlation does not imply causation"? I can't see the difference, myself; perhaps you could explain how this differs?

Surely a more valid test would require a far larger dataset, something like all the published results (that are, or could be made to look like, frequencies or periods) you have read, or heard of, since you were first interested in this ATM idea? IOW, a variation on the classic "wow! you have the same birthday as I do! how unlikely is that!!" (I'm sure you know what the size of a group of people, with birthdays randomly distributed throughout the year, required for the answer to be >0.5) ... you must have read, or seen, hundreds of thousands of values, even in the years between 1978 and 1994 ... yet the only one you chose to do your statistical analysis on was one that is similar to your target.

Generalising your test: suppose we find another coincidence (it could even be closer, say p<10^-100) between a value predicted by some numerologist and something published in an astronomical journal. How accurate is it to say that the only 'rtomes test' of the validity of this coincidence is that there was no prior communication between the two parties?

Moderator note: Moved from the Harmonics Theory thread, per the OP’s request.

How important is it to be very careful to:

* check Tifft's calculations?
* include Tifft's estimates of uncertainty (both random and systematic)?
* determine how strong the period is, using either Tifft's own metric, or an independent one?
* check the consistency of Tifft's results, between papers?Can you please confirm that the predicted periods are all exact?I need a clarification here.

If I have a timeseries with a strong period of n, then any (most?) analyses of this will also show periods of all integer multiples of n, right?

For example, if I have 100 years' of observational data on the magnitude of an eclipsing binary with a period of 2.37 days (say), then an FFT of that data will show peaks at 4.74, 7.11, 9.48, ... days won't it?

So shouldn't any statistical analysis focus only on incommensurate periods?According to your website, the Tifft periods are "72, 36, 24, 18, 16, 9.0, 8.0, 6.0, 3.0" km/s. Of which the only non-degenerates ones are 3.0 and 8.0.

According to post #92, the only non-degenerate peaks labelled are 3.006 and 4.008. However, there also seem to be ~5 other peaks at least as strong as 2.672, which are not labelled.

What criteria should be used to select the peaks for testing?In light of the degenerate values, we need test only Tifft 3.0 and 8.0, and tomes 3.006 and 4.008 ... right?In light of the degeneracies, isn't it (log(100)-log(2))/log(1.005)/2/2 (not .../9)? And don't we also need to somehow exclude all the degenerate values (range 3 to 5 km/s, for example)? And why log(2) (shouldn't it be log(3))? And don't we need to factor in the estimated uncertainties of the Tifft values?

When correlation exists without causation then there is a common cause. That is good enough.

One set of results is a set of measurements that claims to show periodicity in galaxy spacings. The other is a a theory that predicts periodicities in galaxy spacings. If they match at a ridiculous level of improbability then you give me any explanation that will work for explaining that. The one purports to predict the other. If it does, you can argue about the details of interpretation, but the fact would be that it does.
Even if I had seen 1000 other results and ignored them, a p<10^-18 result would still be a p<10^-15 result. Good enough?

However I have mentioned all the results that I know of that are between 2 km/s and 100 km/s. Apart from the 72 km/s which has been reported by many people, the only other one I now of is Guthrie and Napier at 37.6+/-2.x which simply confirms Tifft's 36.

I do think that it is fair to not include Tifft's results after he developed his own theory. He continued to get the original periods plus some extra suggested by his theory. Some of these match harmonics theory and some do not.
If the numerologist can show a simple method that will produce accurate astronomical data at that level then I will start believing in numerology. But I am not holding my breath.

Moderator note: Moved from the Harmonics Theory thread, per the OP’s request.

There is already a thread, started by you, devoted to 'quantized redshifts'. That thread contains many posts on Tifft's work. If you like, I will move the two/three posts in this thread on Tifft (etc) to the other thread.

In any case, I will not continue a discussion of these matters in this thread.

Moderator note: Moved from the Harmonics Theory thread, per the OP’s request.

Stephen E. Schneider and Edwin E. Salpeter, Velocity differences in binary galaxies ... AstroPhys J 385:32-48, 1992 Jan 20

W. J. Cocke and W. G. Tifft, Redshift Quantization in Compact Groups of Galaxies AstroPhys J 268:56-59, 1983 May 1

Halton Arp and Jack W. Sulentic, Ananlysis of Groups of Galaxies with accurate Redshifts, AstroPhys J 291:88-111, 1985 April 1

Guthrie and Napier, Quantized Redshifts: A Status Report, J. Astrophys. Astr. (1997) 18, 455–463
http://www.ias.ac.in/jarch/jaa/18/455-463.pdf
(They found both 72 km/s and 36 km/s approx)
It doesn't exist, that is why so many people keep finding it.
Arp, Guthrie, Napier, Cocke, Tifft, Sulentic, Burbidge, Hoyle, Schneider, Salpeter, ... are all deluded.
Tifft's mentions that there are three aspects to the quanta: within a galaxy; within a group; and over the whole sky. There are various issues associated with each. The within a group velocity quanta are the most easy to find. The within a galaxy ones are tricky because there is the rotation curve to deal with. I do not want to get into those issues because I do not know enough about them. The over the whole sky ones are a bit tricky also as you have to work out our velocity relative to the rest frame.

Therefore I suggest sticking mainly to the within a group papers as being simpler to understand. I do think that Tifft's whole sky thing is correct, but I don't want to deal with things like the 18 km/s galaxy expansion because I do not know enough about the reason for it. I suggest that it is simply a means for Tifft to get from the CMBR frame to his preferred frame. While that explanation would be interesting, it is not needed for my purposes. I only care that there is some frame in which it happens, and Tifft has found that.

The questions that you ask all disappear for the within a group studies because we have a common motion relative to all the group. They are relevent to within a galaxy so I suggest to leave those ones aside. The 18 km/s gaalxy expansion is related to understanding why the CMBR frame is not the same as Tifft's frame but not relevent to whether there are redshifts in that frame.
I hope that I have addressed these to your satisfaction above.
I have given a Napier and Guthrie reference above. It is a later paper than the one I mentioned, being a review that includes additional stuff.

Yes, I expect that the Andromeda distance is likely to be one of the distance quanta. Likewise for the Magellanic clouds. It might be 36 and 3 or 72 and 6 km/s in velocity units. I know that M31 has a redshift interpreted as approaching us. However Arp has shown that in general the largest galaxies in a group are blueshifted relative to the group average. In terms of Arp and Narlikar's theory this can be interpreted as them having an internal blueshift.

I highlighted "distance" above because I think there are both distance and redshift periodicities, and they are obviously strongly correlated for galaxies (much less so for quasars). However there are some small components for galaxies that are neither distance nor velocity and which are best interpreted as what Arp calls internal redshift. That is, they have faster atomic vibrations. This can be understood in harmonics theory because the larger galaxy is often at the centre of a group and generally has its atomic waves in touch with more nearby matter and for longer (being also older).
I think that people like Arp and Tifft are getting quite old. Hoyle is dead. They have seen a way forward, especially Hoyle, Arp and Narlikar, but the herd has gone another way. I would like to try and change that. I am not so young either.

The Harmonics theory is probably easier to get astronomers to believe in without quantized redshifts, if that is what you mean. In that respect I might have been better to do (other aspects of) harmonics theory first and then quantized redshifts later. Too late now! Faint heart never won fair lady!

I have answered this in a post just made which describes three different aspects of redshift by Tifft. Just to clarify, these are all concerned with internal variations within a galaxy. I do not know enough about this to make sensible comments as it involves rotation curves and such. So I do not say it is wrong, but I can defend the other two much better.

I would like you to look at the 128 Mpc periodicity graphic that I posted and address that one. I think it is very convincing and such large scale structures were not expected in big bang cosmology but are in Harmonics theory. It is a very clear period based on a large sample. It also shows several shorter periods, with the 4th harmonic being quite obvious.